Sine Power Lindley Distribution with Applications

Sine power Lindley distribution (SPLi), a new distribution with two parameters that extends the Lindley model, is introduced and studied in this paper. The SPLi distribution is more flexible than the power Lindley distribution, and we show that in the application part. The statistical properties of the proposed distribution are calculated, including the quantile function, moments, moment generating function, upper incomplete moment, and lower incomplete moment. Meanwhile, some numerical values of the mean, variance, skewness, and kurtosis of the SPLi distribution are obtained. Besides, the SPLi distribution is evaluated by different measures of entropy such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, Arimoto entropy, and Tsallis entropy. Moreover, the maximum likelihood method is exploited to estimate the parameters of the SPLi distribution. The applications of the SPLi distribution to two real data sets illustrate the flexibility of the SPLi distribution, and the superiority of the SPLi distribution over some well-known distributions, including the alpha power transformed Lindley, power Lindley, extended Lindley, Lindley, and inverse Lindley distributions.